What is the Greatest Common Factor of 21744 and 21759?

Greatest common factor (GCF) of 21744 and 21759 is 3.

GCF(21744,21759) = 3

We will now calculate the prime factors of 21744 and 21759, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 21744 and 21759.

How to find the GCF of 21744 and 21759?

We will first find the prime factorization of 21744 and 21759. After we will calculate the factors of 21744 and 21759 and find the biggest common factor number .

Step-1: Prime Factorization of 21744

Prime factors of 21744 are 2, 3, 151. Prime factorization of 21744 in exponential form is:

21744 = 2⁴ × 3² × 151¹

Step-2: Prime Factorization of 21759

Prime factors of 21759 are 3, 7253. Prime factorization of 21759 in exponential form is:

21759 = 3¹ × 7253¹

Step-3: Factors of 21744

List of positive integer factors of 21744 that divides 21744 without a remainder.

1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144, 151, 302, 453, 604, 906, 1208, 1359, 1812, 2416, 2718, 3624, 5436, 7248, 10872

Step-4: Factors of 21759

List of positive integer factors of 21759 that divides 21744 without a remainder.

1, 3, 7253

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 21744 and 21759. The biggest common factor number is the GCF number.
So the greatest common factor 21744 and 21759 is 3.

Also check out the Least Common Multiple of 21744 and 21759